The USSR went through an extensive demobilisation process following the war. This was part of the vast, and generally quite successful, programme of reconstruction that retooled and rebuilt the economy. By 1950 the Soviet economic production had surpassed its pre-war levels. But on to the soldiers.

From a starting point of 11m Soviet soldiers in 1945, at least 8.5m were demobilised in batches over the period 1945-48. As was typical in the USSR, the process was 'difficult' (to quote Harrison) with the state simply unable to manage the transportation and promised material support of returning veterans. (That 1946-47 were also famine years didn't help.) Many soldiers were simply handed their papers and told to make their own way home.

But if these were years of hardship then at least employment was not a problem. If the veterans did not return home as a privileged cohort (and the degree to which they did is still debated) they had the advantage of a strong labour market. Labour shortages had emerged as a chronic feature of the Soviet economy in the pre-war years and the immense loss of life during the war had only sharpened this. The returning veterans did not come close to filling this gap, hence migration of peasant labour continued to be a feature of the post-war economy.

Crucially, demobilisation furthered this shift towards an urban economy. Approximately half of all veterans found their way into the cities, as part of the industrial workforce. Given that most soldiers had been recruited from the peasantry, this itself represented a significant demographic shift. Flitzer has some detailed figures on industry recruitment (see below, I unfortunately don't have the source to hand) but by and large they would have followed the patterns of pre-war industrial growth - eg metallurgy, mining, construction, etc.

I can't say how many career soldiers emerged from the war. From a macro perspective however, the Soviet economy never entirely demobilised. Many of the war industries, and formations obviously, were maintained into the Cold War. Despite a brief respite under Khrushchev (with a further round of demobilisations in 1953-60) the USSR emerged from the war with an economic 'defence burden' as high, or higher, than that of 1940.

Sources

Obviously my background is largely the economic and social impact of the war and demobilisation. In this I'm primarily drawing on Donald Filtzer (Soviet Workers and Late Stalinism), Mark Harrison (The Soviet Union After 1945, The Soviet Industrial Defence Complex in WWII) and Michael Ellman (Socialist Planning).

I've not read it myself but I've heard good things about Mark Edele's Soviet Veterans of the Second World War. I suspect that that work would answer most of your questions.